Hide/show radio buttons stop working on save - wordpress

Question

Here's my case: I'm developing a little widget, and I was looking for a way to hide/show different DIVs on selecting a set of radio buttons. I found the proper code and adjusted it to my needs. The only problem is that the hide/show feature stops working after clicking on save while configuring the widget :S
Here's the JS:
jQuery(document).ready(function($) {
$(document).ready(function() {
$('input[type="radio"]').click(function(){
if($(this).attr("value")=="link_to_image"){
$(".radio-option").hide();
$(".linked-image").show();
}
if($(this).attr("value")=="link_to_page"){
$(".radio-option").hide();
$(".linked-page").show();
}
});
});
});
And the HTML:
<p>
<label>Link:</label><br>
<label>
<input type="radio" name="link_to" value="link_to_image">
Link to image
</label><br>
<label>
<input type="radio" name="link_to" value="link_to_page">
Link to page
</label>
</p>
<div class="linked-image radio-option">
<label for="linked_image">Linked image:</label>
<p>
Content for linked_image DIV
</p>
</div>
<div class="linked-page radio-option">
<label for="linked_page">Linked page:</label>
<p>
Content for linked_page DIV
</p>
</div>
And the [JSFiddle] (http://jsfiddle.net/ccwsy5z4/)
Could you give me a hand with this, guys?

Answer 1

So finally I found out that the problem was that the JS stopped working after the AJAX started by clicking on the Save button.
And the solution for that was to recall the JS function after AJAX finished it job. To do that first I had to give a name to the JS function, called it after that, and then call it again after AJAX stopped. Like this:
jQuery(document).ready(function($) {
function radioButtonShow() {
if($(this).attr("value")=="link_to_image") {
$(".radio-option").hide();
$(".linked-image").show();
}
if($(this).attr("value")=="link_to_page") {
$(".radio-option").hide();
$(".linked-page").show();
}
};
$('input[type="radio"]').click(radioButtonShow);
$(document).ajaxStop(function() {
$('input[type="radio"]').click(radioButtonShow);
});
});
Hope this may be useful to somebody :)